Quantum Dynamics of Vortices and Vortex Qubits

Abstract

Vortices appear naturally in a wide range of gases and fluids, both on very large scales, e.g. when tornadoes form in the Earth’s atmosphere, and on very small scales, e.g. in Bose– Einstein condensates of dilute atomic gases [1] or in superfluid helium [2], where their existence is a consequence of the quantum nature of the liquid. Collective nonlinear excitations such as the vortex considered here are ubiquitous in solid state systems (e.g. domain walls) and biological systems (e.g. waves on membranes), and have even been considered as model systems in particle physics. In superconductors, which we consider here, quantized vortices of the supercurrent [3], which are generated by magnetic flux penetrating into the material, play a key role in understanding the material properties [4] and the performance of superconductorbased devices [5,6]. At high temperatures the dynamics of vortices is essentially classical. At low temperatures, however, there are experiments suggesting the collective quantum dynamics of vortices [7,8]. Here we report on experiments in which we have probed for the first time the quantum dynamics of an individual vortex in a superconductor. By measuring the statistics of the vortex escape from a controllable pinning potential, we were able to demonstrate the quantization of the vortex energy within the trapping potential well and the quantum tunneling of the vortex through the pinning barrier. The object that we have studied in our experiments is a vortex of electric current with a spatial extent of several tens of micrometers formed in a long superconducting tunnel junction. The electrodynamics of such a Josephson junction is governed by the phase difference φ between the macroscopic wave functions describing the superconducting condensate in the two electrodes [9]. It is a well established fact that the variable φ displays macroscopic quantum properties in point-like junctions at very low temperatures [10, 11]. Such macroscopic quantum phenomena are currently exploited for quantum information processing [12] using superconducting devices [10, 13–20]. In extended oneor two-dimensional Josephson junction systems, quantum tunneling in real space is to be expected for superconducting vortices, which are particle-like collective excitations of the phase difference φ. The small value of the expected mass of the vortex studied here suggests that quantum effects are likely to occur with vortices at low temperatures. Dissipative vortex tunneling has been given as a reason